The attack you asked about was (from a boss), "WHY are YOU LATE every single morning??! WHY can't you get here on TIME once in a while??!" It's two VAPs in a row -- two examples of the same pattern. The open attack (the bait) in the first one is the presupposition that you're late every morning without exception ; the open attack in the second one is the presupposition that you're not able to get to work on time, ever. The sheltered attack in both is the presupposition -- carried by the heavily-stressed "WHY"-- that no matter what your answer to the question is, it's not good enough.
Let's start by separating the non-emotional message in the VAP from the emotional message. The non-emotional message is "You're late every single morning. You can't ever get here on time, and I want you to tell me why." The emotional message, carried by the tune the words are set to, is totally hostile; it's something like "You're a rotten stinking employee, so unworthy of any respect from me that I have a right to yell at you and do my best to humiliate you in public. I have a right to demand that you answer my hostile questions -- and I want you to know in advance that whatever answer you give me, it's not good enough." Verbal abusers in our culture, when accused of verbal violence, rely on being able to say "But all I said was...." followed by the non-emotional message -- that is, the same words they said in the attack, but set to a tune so different that the hostile emotional message is no longer there.
It makes a difference whether the non-emotional message is accurate -- if you really ARE always late, that's a different matter. Let's assume that it's not true and that you're usually on time. Whether using a BBR will, as you suggest, make things worse or not depends on the boss, on you, and on the situation. In some cases it will work very well -- but that's a different topic. [You can read about the BBR, if the term is new to you, by going to http://www.howthingswork.com
and typing "verbal self-defense" into the search box.] Let's assume that it won't work in the case you're describing.
The most likely appropriate move is for you to go straight to Computer Mode and stay there. That means four things: speaking in platitudes and generalities and hypotheticals; saying things that no rational person could argue with; getting rid of as much personal language (I, you, this office, this company, me, etc.) as possible; and being very careful to set your words to neutral tunes. Your goal is to distract the boss from the anger aimed specifically at you and shift him or her to a different topic; you want to talk the boss down. Here's a possible scenario, with your utterances constructed to meet the four specifications; every word you say has been carefully chosen and is used for very good reasons.
Boss: "WHY are YOU LATE every single morning??! WHY can't you get here on TIME once in a while??!"
You: "Bosses who believe their employees always come in late can really get upset about that."
Boss: "Damn RIGHT! And they'd have to be crazy NOT to get upset!"
You: "Nobody could argue with that. If employees are late, it's hard on the company."
Boss: "It's a damn waste of MY MONEY! It makes my BLOOD boil!"
You: "Being angry all the time is dangerous; it can make people really sick."
Boss: "Oh, that's a bunch of New Age GARbage! DON'T give me that!"
You: "There's solid research showing that people who are always angry are in serious danger from heart attacks and stroke."
Boss: "Oh, yeah? What research is that?"
(And so on.)
This almost always works, provided you stick to it and refuse to be tempted into counter-attacking and taking the bait. It won't take any longer than having a fight would take, and it has longterm benefits. People who discover that attacking you never works will give up attacking you. If you find it hard to come up with Computer Mode off the top of your head, do what you'd do with any other martial arts tactic -- _practice_. Write down the attacks that come your way, attacks you hear about from others, attacks you see people use on television, attacks you make up; write Computer Mode responses that you could use to respond to those attacks. Get somebody to do some role-playing with you; have them try to provoke you while you try to stay in Computer Mode. All the resources for using Computer Mode are stored in your mental grammar; you just have to get used to using them, so that they'll be on automatic when you need them.